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Search for a spin-nematic phase in the quasi-one-dimensional frustrated magnet LiCuVO$_4$

We have performed NMR experiments on the quasi one-dimensional frustrated spin-1/2 system LiCuVO$_4$ in magnetic fields $H$ applied along the c-axis up to field values near the saturation field $H_{\rm sat}$. For the field range $H_{\rm c2}<H<H_{\rm c3}$ ($μ_0H_{\rm c2}\approx 7.5$T and $μ_0H_{\rm c3} = [40.5 \pm 0.2]$T) the $^{51}$V NMR spectra at $T$ = 380mK exhibit a characteristic double-horn pattern, as expected for a spin-modulated phase in which the magnetic moments of Cu$^{2+}$ ions are aligned parallel to the applied field $H$ and their magnitudes change sinusoidally along the magnetic chains. For higher fields, the $^{51}$V NMR spectral shape changes from the double-horn pattern into a single Lorentzian line. For this Lorentzian line, the internal field at the $^{51}$V nuclei stays constant for $μ_0 H > 41.4$T, indicating that the majority of magnetic moments in LiCuVO$_4$ are already saturated in this field range. This result is inconsistent with the previously observed linear field dependence of the magnetization $M(H)$ for $H_{\rm c3}<H<H_{\rm sat}$ with $μ_0H_{\rm sat}=45$T [L. E. Svistov {\it et al}., JETP Letters {\bf 93}, 21 (2011)]. We argue that the discrepancy is due to non-magnetic defects in the samples. The results of the spin-lattice relaxation rate of $^7$Li nuclei indicate an energy gap which grows with field twice as fast as the Zeeman energy of a single spin, therefore, suggesting that the two-magnon bound state is the lowest energy excitation. The energy gap tends to close at $μ_0H \approx 41$T. Our results suggest that the theoretically predicted spin-nematic phase, if it exists in LiCuVO$_4$, can be established only within the narrow field range $40.5 < μ_0 H < 41.4$T .